The moves come as Shia Houthi rebels have taken over large parts of the Arab nation and crisis talks broke down this week.
"Due to the uncertain security situation in Sanaa, the Department of State has decided to suspend our embassy operations and our embassy staff have been temporarily relocated out of Sanaa," US State Department spokesperson Jen Psaki said.
Recent unilateral actions disrupted the political transition process in Yemen, creating the risk that renewed violence would threaten Yemenis and the diplomatic community in Sanaa, she said.
Psaki said the US will continue to engage Yemenis and the international community to support Yemen's political transition process, consistent with the Gulf Cooperation Council Initiative, the outcomes of the National Dialogue Conference, UN Security Council resolutions and Yemeni law.
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"We reiterate the call of the United Nations Security Council for immediate release of President Hadi, Prime Minister Bahah, and members of the Yemeni cabinet. An inclusive political process cannot resume with members of the country's leadership under house arrest," Psaki said.
"The security situation in Yemen has continued to deteriorate over recent days," UK minister for the Middle East Tobias Ellwood said.
"Regrettably we now judge that our embassy staff and premises are at increased risk. We have therefore decided to withdraw diplomatic staff and temporarily suspend the operations of the British embassy in Sanaa. Our Ambassador and diplomatic staff have left Yemen this morning and will return to the UK," he added.
The volatile situation in Yemen escalated last month when the Houthis seized a key aide of President Hadi, in an attempt to block a draft constitution.
UN-organised crisis talks between the country's political factions broke down this week, with the two parties citing "threats" from the Houthi rebels.